Eq. (REF ) imposes a strict relation, in any noncontextual model and beyond the ideal scenario, between the \(\ell _1\)  distance of two epistemic states and their operationally accessible confusability. Hence, we anticipate that these relations will be of broader use to identify quantum advantages beyond state-dependent cloning. For instance, following the same reasoning given after Theorem REF , these inequalities provide an alternative and intuitive derivation of the tight noise-robust noncontextual bound on state discrimination of Ref. [1]},
\(s_{ab}\le \frac{1}{2} + \frac{1}{4} \Vert \mu _a - \mu _b\Vert  \le 1 - \frac{c_{ab}-\epsilon _b}{2}\) .
